The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1 3X+2 3X 3X  2  X X+2  1  1 3X  1  1  1  1  0  1 2X+2  1  1
 0  1  0 2X 2X+3  3  1  X 2X+2 3X+3 X+1  1  2  1  1  1  X X+2 2X+3  1 3X+3 3X+1  X  1  X  2  1 2X  0
 0  0  1 3X+1 X+1 2X 3X+1 3X  1 X+3 3X+2 X+2  1 X+1  3 2X+2  1 2X+3  3 2X+3  1  2 X+3  X  1 3X+3 3X 3X+3  2

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+174x^26+924x^27+622x^28+960x^29+384x^30+704x^31+175x^32+80x^33+50x^34+20x^35+2x^36

The gray image is a code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.16 in 0.079 seconds.